A couple of weeks before the French Open, the question of who might replace Ivan Lendl as Andy Murray's coach, following a lengthy interregnum, was discussed on Radio 4's Today programme. There had been rumours that Amélie Mauresmo might be in the frame for the job, but the male pundit brought on to discuss the story was dismissive. There was nothing in it, he promised. While the prospect seemed intriguing, he pointed out that it was "one thing being coached by your mum when you're a child", and quite another taking advice from a woman when you're gunning for grand slams.

No one on the programme challenged this casual remark. No one pointed out the insult that it concealed to Judy Murray, an international tennis coach and captain of the British Fed Cup team – and to Mauresmo, a winner of Wimbledon and the Australian Open and a former world No 1, who probably has more experience and understanding of what Murray faces at the summit of his career than some of his previous coaches (Brad Gilbert, Mark Petchey, Miles Maclagan reached numbers 4, 80 and 172 respectively). Let us not forget that Lendl's appointment as Murray's coach was greeted with approval because he was someone who knew what it was like to win grand slams.

The confirmation of Mauresmo's appointment on Sunday, and the fact that said pundits had, in their shortsightedness, overlooked the biggest Murray scoop since Lendl's departure, is some comfort. Even more enjoyable was Murray's own reaction. Phlegmatic to the point of downbeat, Murray treated the news with the same what-does-it-matter-to-you response that characterises his attitude to all media fascination with him. His praise of Mauresmo and her suitability for the role was rendered in low-key terms; he referred to the specific skills and temperament that he thinks will make them compatible. "She's very calm," he said. "She's a good person, I think we'll communicate well together." The idea that it's strange to ask a woman to coach a man at tennis is presumably based on a muddled notion that Mauresmo would be unable to understand the different pace or skills required in the men's game (even if the same delineations would have her down as part of the "more empathetic" gender). But professional football, rugby, baseball, cricket and basketball teams are often managed by people who have never personally experienced playing the same level of sport they are coaching.

At a time when the appointment of women to positions of influence is a contentious and enduring topic, this was a significant moment made all the more pleasing by its entire lack of hype and hysteria. The handwringing of the phrase "we need more women in … " (politics, technology, football, FTSE 100 companies) has become, even for women, a bit of a turn-off, with its suggestion that women are primarily a problem to be solved. Then there are the quotas, called for when an impassable level of frustration, or even desperation, is reached. The overwhelming maleness of TV panel games inspired Danny Cohen, director of BBC television, to announce that every BBC comedy panel show must henceforth include a woman. Cue complaints that there isn't enough female talent ready for the job.

Entrenched systems of exclusion need to be challenged, of course, but this appointment showed how utterly irrelevant a quota can seem when someone who needs a specific skill set goes looking for it. Mauresmo wasn't appointed as part of a drive for more women in tennis coaching, or because a sports body was likely to lose its funding if it failed to promote diversity. Murray chose her because he thought she would be good at the job and work well with him. With one low-key announcement, he may have scotched as many myths as any number of diversity programmes.